# Operations in the correct order

When you are faced with a mathematical expression that has several operations or parentheses, the solution may be affected by the order in which you tackle the operations. For example, take the expression

$4\xb77-2$

If we do the multiplication first, we arrive at the following answer:

$28-2=26$

If instead we begin by substracting, we get:

$4\xb75=20$

In order to avoid confusion and to ensure that everyone always arrives at the same result, mathematicians established a standard order of operations for calculations that involve more than one arithmetic operation. Arithmetic operations should always be carried out in the following order:

- Simplify the expressions inside parentheses ( ), brackets [ ], braces { } and fractions bars.
- Evaluate all powers.
- Do all multiplications and divisions from left to right.
- Do all additions and subtractions from left to right.

**Example**

Suppose you want to figure out how many hours a person works in two days assuming that they work 4 hours before lunch and 3 hours after lunch each day. First, work out how many hours the person works each day:

$4+3=7$

and then multiply that by the number of days the person worked:

$7\xb72=14$

If we were to write this example as one expression, we would need to use parentheses to make sure that people calculate the addition first:

$\left(4+3\right)\xb72=14$

## Video lesson

Simplify the following expression:

$2\xb7\left[\left(8-3\right)+6\xb7\left(2\right)\right]-3$